Cube-Cut: Vertebral Body Segmentation in MRI-Data through Cubic-Shaped Divergences

In this article, we present a graph-based method using a cubic template for volumetric segmentation of vertebrae in magnetic resonance imaging (MRI) acquisitions. The user can define the degree of deviation from a regular cube via a smoothness value Delta. The Cube-Cut algorithm generates a directed graph with two terminal nodes (s-t-network), where the nodes of the graph correspond to a cubic-shaped subset of the image's voxels. The weightings of the graph's terminal edges, which connect every node with a virtual source s or a virtual sink t, represent the affinity of a voxel to the vertebra (source) and to the background (sink). Furthermore, a set of infinite weighted and non-terminal edges implements the smoothness term. After graph construction, a minimal s-t-cut is calculated within polynomial computation time, which splits the nodes into two disjoint units. Subsequently, the segmentation result is determined out of the source-set. A quantitative evaluation of a C++ implementation of the algorithm resulted in an average Dice Similarity Coefficient (DSC) of 81.33% and a running time of less than a minute.Comment: 23 figures, 2 tables, 43 references, PLoS ONE 9(4): e9338

Three-dimensional Segmentation of the Scoliotic Spine from MRI using Unsupervised Volume-based MR-CT Synthesis

Vertebral bone segmentation from magnetic resonance (MR) images is a challenging task. Due to the inherent nature of the modality to emphasize soft tissues of the body, common thresholding algorithms are ineffective in detecting bones in MR images. On the other hand, it is relatively easier to segment bones from CT images because of the high contrast between bones and the surrounding regions. For this reason, we perform a cross-modality synthesis between MR and CT domains for simple thresholding-based segmentation of the vertebral bones. However, this implicitly assumes the availability of paired MR-CT data, which is rare, especially in the case of scoliotic patients. In this paper, we present a completely unsupervised, fully three-dimensional (3D) cross-modality synthesis method for segmenting scoliotic spines. A 3D CycleGAN model is trained for an unpaired volume-to-volume translation across MR and CT domains. Then, the Otsu thresholding algorithm is applied to the synthesized CT volumes for easy segmentation of the vertebral bones. The resulting segmentation is used to reconstruct a 3D model of the spine. We validate our method on 28 scoliotic vertebrae in 3 patients by computing the point-to-surface mean distance between the landmark points for each vertebra obtained from pre-operative X-rays and the surface of the segmented vertebra. Our study results in a mean error of 3.41 $\pm$ 1.06 mm. Based on qualitative and quantitative results, we conclude that our method is able to obtain a good segmentation and 3D reconstruction of scoliotic spines, all after training from unpaired data in an unsupervised manner.Comment: To appear in the Proceedings of the SPIE Medical Imaging Conference 2021, San Diego, CA. 9 pages, 4 figures in tota

Automatic segmentation of the spine by means of a probabilistic atlas with a special focus on ribs suppression

[EN] Purpose: The development of automatic and reliable algorithms for the detection and segmentation of the vertebrae are of great importance prior to any diagnostic task. However, an important problem found to accurately segment the vertebrae is the presence of the ribs in the thoracic region. To overcome this problem, a probabilistic atlas of the spine has been developed dealing with the proximity of other structures, with a special focus on ribs suppression. Methods: The data sets used consist of Computed Tomography images corresponding to 21 patients suffering from spinal metastases. Two methods have been combined to obtain the final result: firstly, an initial segmentation is performed using a fully automatic level-set method; secondly, to refine the initial segmentation, a 3D volume indicating the probability of each voxel of belonging to the spine has been developed. In this way, a probability map is generated and deformed to be adapted to each testing case. Results: To validate the improvement obtained after applying the atlas, the Dice coefficient (DSC), the Hausdorff distance (HD), and the mean surface-to-surface distance (MSD) were used. The results showed up an average of 10 mm of improvement accuracy in terms of HD, obtaining an overall final average of 15.51 2.74 mm. Also, a global value of 91.01 3.18% in terms of DSC and a MSD of 0.66 0.25 mm were obtained. The major improvement using the atlas was achieved in the thoracic region, as ribs were almost perfectly suppressed. Conclusion: The study demonstrated that the atlas is able to detect and appropriately eliminate the ribs while improving the segmentation accuracy.The authors thank the financial support of the Spanish Ministerio de Economia y Competitividad (MINECO) and FEDER funds under Grants TEC2012-33778 and BFU2015-64380-C2-2-R (D.M.) and DPI2013-4572-R (J.D., E.D.)Ruiz-España, S.; Domingo, J.; Díaz-Parra, A.; Dura, E.; D'ocon-Alcaniz, V.; Arana, E.; Moratal, D. (2017). Automatic segmentation of the spine by means of a probabilistic atlas with a special focus on ribs suppression. Medical Physics. 44(9):4695-4707. https://doi.org/10.1002/mp.12431S46954707449Harris, R. I., & Macnab, I. (1954). STRUCTURAL CHANGES IN THE LUMBAR INTERVERTEBRAL DISCS. The Journal of Bone and Joint Surgery. British volume, 36-B(2), 304-322. doi:10.1302/0301-620x.36b2.304Oliveira, M. F. de, Rotta, J. M., & Botelho, R. V. (2015). Survival analysis in patients with metastatic spinal disease: the influence of surgery, histology, clinical and neurologic status. Arquivos de Neuro-Psiquiatria, 73(4), 330-335. doi:10.1590/0004-282x20150003Chou, R. (2011). Diagnostic Imaging for Low Back Pain: Advice for High-Value Health Care From the American College of Physicians. Annals of Internal Medicine, 154(3), 181. doi:10.7326/0003-4819-154-3-201102010-00008Brayda-Bruno, M., Tibiletti, M., Ito, K., Fairbank, J., Galbusera, F., Zerbi, A., … Sivan, S. S. (2013). Advances in the diagnosis of degenerated lumbar discs and their possible clinical application. European Spine Journal, 23(S3), 315-323. doi:10.1007/s00586-013-2960-9Quattrocchi, C. C., Santini, D., Dell’Aia, P., Piciucchi, S., Leoncini, E., Vincenzi, B., … Zobel, B. B. (2007). A prospective analysis of CT density measurements of bone metastases after treatment with zoledronic acid. Skeletal Radiology, 36(12), 1121-1127. doi:10.1007/s00256-007-0388-1Doi, K. (2007). Computer-aided diagnosis in medical imaging: Historical review, current status and future potential. Computerized Medical Imaging and Graphics, 31(4-5), 198-211. doi:10.1016/j.compmedimag.2007.02.002Ruiz-España, S., Arana, E., & Moratal, D. (2015). Semiautomatic computer-aided classification of degenerative lumbar spine disease in magnetic resonance imaging. Computers in Biology and Medicine, 62, 196-205. doi:10.1016/j.compbiomed.2015.04.028Alomari, R. S., Ghosh, S., Koh, J., & Chaudhary, V. (2014). Vertebral Column Localization, Labeling, and Segmentation. Lecture Notes in Computational Vision and Biomechanics, 193-229. doi:10.1007/978-3-319-12508-4_7Hamarneh, G., & Li, X. (2009). Watershed segmentation using prior shape and appearance knowledge. Image and Vision Computing, 27(1-2), 59-68. doi:10.1016/j.imavis.2006.10.009Ghebreab, S., & Smeulders, A. W. (2004). Combining Strings and Necklaces for Interactive Three-Dimensional Segmentation of Spinal Images Using an Integral Deformable Spine Model. IEEE Transactions on Biomedical Engineering, 51(10), 1821-1829. doi:10.1109/tbme.2004.831540Mastmeyer, A., Engelke, K., Fuchs, C., & Kalender, W. A. (2006). A hierarchical 3D segmentation method and the definition of vertebral body coordinate systems for QCT of the lumbar spine. Medical Image Analysis, 10(4), 560-577. doi:10.1016/j.media.2006.05.005Rasoulian, A., Rohling, R., & Abolmaesumi, P. (2013). Lumbar Spine Segmentation Using a Statistical Multi-Vertebrae Anatomical Shape+Pose Model. IEEE Transactions on Medical Imaging, 32(10), 1890-1900. doi:10.1109/tmi.2013.2268424Ma, J., & Lu, L. (2013). Hierarchical segmentation and identification of thoracic vertebra using learning-based edge detection and coarse-to-fine deformable model. Computer Vision and Image Understanding, 117(9), 1072-1083. doi:10.1016/j.cviu.2012.11.016Kim, Y., & Kim, D. (2009). A fully automatic vertebra segmentation method using 3D deformable fences. Computerized Medical Imaging and Graphics, 33(5), 343-352. doi:10.1016/j.compmedimag.2009.02.006Klinder, T., Ostermann, J., Ehm, M., Franz, A., Kneser, R., & Lorenz, C. (2009). Automated model-based vertebra detection, identification, and segmentation in CT images. Medical Image Analysis, 13(3), 471-482. doi:10.1016/j.media.2009.02.004Štern, D., Likar, B., Pernuš, F., & Vrtovec, T. (2011). Parametric modelling and segmentation of vertebral bodies in 3D CT and MR spine images. Physics in Medicine and Biology, 56(23), 7505-7522. doi:10.1088/0031-9155/56/23/011Korez, R., Ibragimov, B., Likar, B., Pernus, F., & Vrtovec, T. (2015). A Framework for Automated Spine and Vertebrae Interpolation-Based Detection and Model-Based Segmentation. IEEE Transactions on Medical Imaging, 34(8), 1649-1662. doi:10.1109/tmi.2015.2389334Castro-Mateos, I., Pozo, J. M., Pereanez, M., Lekadir, K., Lazary, A., & Frangi, A. F. (2015). Statistical Interspace Models (SIMs): Application to Robust 3D Spine Segmentation. IEEE Transactions on Medical Imaging, 34(8), 1663-1675. doi:10.1109/tmi.2015.2443912Pereanez, M., Lekadir, K., Castro-Mateos, I., Pozo, J. M., Lazary, A., & Frangi, A. F. (2015). Accurate Segmentation of Vertebral Bodies and Processes Using Statistical Shape Decomposition and Conditional Models. IEEE Transactions on Medical Imaging, 34(8), 1627-1639. doi:10.1109/tmi.2015.2396774Michael Kelm, B., Wels, M., Kevin Zhou, S., Seifert, S., Suehling, M., Zheng, Y., & Comaniciu, D. (2013). Spine detection in CT and MR using iterated marginal space learning. Medical Image Analysis, 17(8), 1283-1292. doi:10.1016/j.media.2012.09.007Yan Kang, Engelke, K., & Kalender, W. A. (2003). A new accurate and precise 3-D segmentation method for skeletal structures in volumetric CT data. IEEE Transactions on Medical Imaging, 22(5), 586-598. doi:10.1109/tmi.2003.812265Huang, J., Jian, F., Wu, H., & Li, H. (2013). An improved level set method for vertebra CT image segmentation. BioMedical Engineering OnLine, 12(1), 48. doi:10.1186/1475-925x-12-48Lim, P. H., Bagci, U., & Bai, L. (2013). Introducing Willmore Flow Into Level Set Segmentation of Spinal Vertebrae. IEEE Transactions on Biomedical Engineering, 60(1), 115-122. doi:10.1109/tbme.2012.2225833Forsberg, D., Lundström, C., Andersson, M., & Knutsson, H. (2013). Model-based registration for assessment of spinal deformities in idiopathic scoliosis. Physics in Medicine and Biology, 59(2), 311-326. doi:10.1088/0031-9155/59/2/311Yao, J., Burns, J. E., Forsberg, D., Seitel, A., Rasoulian, A., Abolmaesumi, P., … Li, S. (2016). A multi-center milestone study of clinical vertebral CT segmentation. Computerized Medical Imaging and Graphics, 49, 16-28. doi:10.1016/j.compmedimag.2015.12.006Shi, C., Wang, J., & Cheng, Y. (2015). Sparse Representation-Based Deformation Model for Atlas-Based Segmentation of Liver CT Images. Image and Graphics, 410-419. doi:10.1007/978-3-319-21969-1_36Domingo, J., Dura, E., Ayala, G., & Ruiz-España, S. (2015). Means of 2D and 3D Shapes and Their Application in Anatomical Atlas Building. Lecture Notes in Computer Science, 522-533. doi:10.1007/978-3-319-23192-1_44Hyunjin Park, Bland, P. H., & Meyer, C. R. (2003). Construction of an abdominal probabilistic atlas and its application in segmentation. IEEE Transactions on Medical Imaging, 22(4), 483-492. doi:10.1109/tmi.2003.809139Cabezas, M., Oliver, A., Lladó, X., Freixenet, J., & Bach Cuadra, M. (2011). A review of atlas-based segmentation for magnetic resonance brain images. Computer Methods and Programs in Biomedicine, 104(3), e158-e177. doi:10.1016/j.cmpb.2011.07.015Fortunati, V., Verhaart, R. F., van der Lijn, F., Niessen, W. J., Veenland, J. F., Paulides, M. M., & van Walsum, T. (2013). Tissue segmentation of head and neck CT images for treatment planning: A multiatlas approach combined with intensity modeling. Medical Physics, 40(7), 071905. doi:10.1118/1.4810971Zhuang, X., Bai, W., Song, J., Zhan, S., Qian, X., Shi, W., … Rueckert, D. (2015). Multiatlas whole heart segmentation of CT data using conditional entropy for atlas ranking and selection. Medical Physics, 42(7), 3822-3833. doi:10.1118/1.4921366Zhou, J., Yan, Z., Lasio, G., Huang, J., Zhang, B., Sharma, N., … D’Souza, W. (2015). Automated compromised right lung segmentation method using a robust atlas-based active volume model with sparse shape composition prior in CT. Computerized Medical Imaging and Graphics, 46, 47-55. doi:10.1016/j.compmedimag.2015.07.003Linguraru, M. G., Sandberg, J. K., Li, Z., Shah, F., & Summers, R. M. (2010). Automated segmentation and quantification of liver and spleen from CT images using normalized probabilistic atlases and enhancement estimation. Medical Physics, 37(2), 771-783. doi:10.1118/1.3284530Xu, Y., Xu, C., Kuang, X., Wang, H., Chang, E. I.-C., Huang, W., & Fan, Y. (2016). 3D-SIFT-Flow for atlas-based CT liver image segmentation. Medical Physics, 43(5), 2229-2241. doi:10.1118/1.4945021Michopoulou, S. K., Costaridou, L., Panagiotopoulos, E., Speller, R., Panayiotakis, G., & Todd-Pokropek, A. (2009). Atlas-Based Segmentation of Degenerated Lumbar Intervertebral Discs From MR Images of the Spine. IEEE Transactions on Biomedical Engineering, 56(9), 2225-2231. doi:10.1109/tbme.2009.2019765Taso, M., Le Troter, A., Sdika, M., Ranjeva, J.-P., Guye, M., Bernard, M., & Callot, V. (2013). Construction of an in vivo human spinal cord atlas based on high-resolution MR images at cervical and thoracic levels: preliminary results. Magnetic Resonance Materials in Physics, Biology and Medicine, 27(3), 257-267. doi:10.1007/s10334-013-0403-6Lévy, S., Benhamou, M., Naaman, C., Rainville, P., Callot, V., & Cohen-Adad, J. (2015). White matter atlas of the human spinal cord with estimation of partial volume effect. NeuroImage, 119, 262-271. doi:10.1016/j.neuroimage.2015.06.040Hardisty, M., Gordon, L., Agarwal, P., Skrinskas, T., & Whyne, C. (2007). Quantitative characterization of metastatic disease in the spine. Part I. Semiautomated segmentation using atlas-based deformable registration and the level set method. Medical Physics, 34(8), 3127-3134. doi:10.1118/1.2746498Forsberg, D. (2015). Atlas-Based Registration for Accurate Segmentation of Thoracic and Lumbar Vertebrae in CT Data. Lecture Notes in Computational Vision and Biomechanics, 49-59. doi:10.1007/978-3-319-14148-0_5Ibañez MV Schroeder W Cates L Insight software Consortium. The ITK Software Guide 2016 http://www.itk.org/ItkSoftwareGuide.pdfLoader C R package: Local regression, likelihood and density estimation. CRAN repository 2013 2016 http://cran.r-project.org/web/packages/locfitPARK, H., HERO, A., BLAND, P., KESSLER, M., SEO, J., & MEYER, C. (2010). Construction of Abdominal Probabilistic Atlases and Their Value in Segmentation of Normal Organs in Abdominal CT Scans. IEICE Transactions on Information and Systems, E93-D(8), 2291-2301. doi:10.1587/transinf.e93.d.2291Pohl, K. M., Fisher, J., Bouix, S., Shenton, M., McCarley, R. W., Grimson, W. E. L., … Wells, W. M. (2007). Using the logarithm of odds to define a vector space on probabilistic atlases. Medical Image Analysis, 11(5), 465-477. doi:10.1016/j.media.2007.06.003Baddeley, A., & Molchanov, I. (1998). Journal of Mathematical Imaging and Vision, 8(1), 79-92. doi:10.1023/a:1008214317492De Bruijne, M., van Ginneken, B., Viergever, M. A., & Niessen, W. J. (2003). Adapting Active Shape Models for 3D Segmentation of Tubular Structures in Medical Images. Information Processing in Medical Imaging, 136-147. doi:10.1007/978-3-540-45087-0_12Zhang, K., Zhang, L., Song, H., & Zhou, W. (2010). Active contours with selective local or global segmentation: A new formulation and level set method. Image and Vision Computing, 28(4), 668-676. doi:10.1016/j.imavis.2009.10.009Kalpathy-Cramer, J., Awan, M., Bedrick, S., Rasch, C. R. N., Rosenthal, D. I., & Fuller, C. D. (2013). Development of a Software for Quantitative Evaluation Radiotherapy Target and Organ-at-Risk Segmentation Comparison. Journal of Digital Imaging, 27(1), 108-119. doi:10.1007/s10278-013-9633-4Huttenlocher, D. P., Klanderman, G. A., & Rucklidge, W. J. (1993). Comparing images using the Hausdorff distance. IEEE Transactions on Pattern Analysis and Machine Intelligence, 15(9), 850-863. doi:10.1109/34.232073Aspert, N., Santa-Cruz, D., & Ebrahimi, T. (s. f.). MESH: measuring errors between surfaces using the Hausdorff distance. Proceedings. IEEE International Conference on Multimedia and Expo. doi:10.1109/icme.2002.103587

Lumbar Model Generator:a tool for the automated generation of a parametric scalable model of the lumbar spine

Low back pain is a major cause of disability and requires the development of new devices to treat pathologies and improve prognosis following surgery. Understanding the effects of new devices on the biomechanics of the spine is crucial in the development of new effective and functional devices. The aim of this study was to develop a preliminary parametric, scalable and anatomically accurate finite-element model of the lumbar spine allowing for the evaluation of the performance of spinal devices. The principal anatomical surfaces of the lumbar spine were first identified, and then accurately fitted from a previous model supplied by S14 Implants (Bordeaux, France). Finally, the reconstructed model was defined according to 17 parameters which are used to scale the model according to patient dimensions. The developed model, available as a toolbox named the lumbar model generator, enables generating a population of models using subject-specific dimensions obtained from data scans or averaged dimensions evaluated from the correlation analysis. This toolbox allows patient-specific assessment, taking into account individual morphological variation. The models have applications in the design process of new devices, evaluating the biomechanics of the spine and helping clinicians when deciding on treatment strategies.</jats:p

Applications of a Biomechanical Patient Model for Adaptive Radiation Therapy

Biomechanical patient modeling incorporates physical knowledge of the human anatomy into the image processing that is required for tracking anatomical deformations during adaptive radiation therapy, especially particle therapy. In contrast to standard image registration, this enforces bio-fidelic image transformation. In this thesis, the potential of a kinematic skeleton model and soft tissue motion propagation are investigated for crucial image analysis steps in adaptive radiation therapy. The first application is the integration of the kinematic model in a deformable image registration process (KinematicDIR). For monomodal CT scan pairs, the median target registration error based on skeleton landmarks, is smaller than (1.6 ± 0.2) mm. In addition, the successful transferability of this concept to otherwise challenging multimodal registration between CT and CBCT as well as CT and MRI scan pairs is shown to result in median target registration error in the order of 2 mm. This meets the accuracy requirement for adaptive radiation therapy and is especially interesting for MR-guided approaches. Another aspect, emerging in radiotherapy, is the utilization of deep-learning-based organ segmentation. As radiotherapy-specific labeled data is scarce, the training of such methods relies heavily on augmentation techniques. In this work, the generation of synthetically but realistically deformed scans used as Bionic Augmentation in the training phase improved the predicted segmentations by up to 15% in the Dice similarity coefficient, depending on the training strategy. Finally, it is shown that the biomechanical model can be built-up from automatic segmentations without deterioration of the KinematicDIR application. This is essential for use in a clinical workflow

Multi-Surface Simplex Spine Segmentation for Spine Surgery Simulation and Planning

This research proposes to develop a knowledge-based multi-surface simplex deformable model for segmentation of healthy as well as pathological lumbar spine data. It aims to provide a more accurate and robust segmentation scheme for identification of intervertebral disc pathologies to assist with spine surgery planning. A robust technique that combines multi-surface and shape statistics-aware variants of the deformable simplex model is presented. Statistical shape variation within the dataset has been captured by application of principal component analysis and incorporated during the segmentation process to refine results. In the case where shape statistics hinder detection of the pathological region, user-assistance is allowed to disable the prior shape influence during deformation. Results have been validated against user-assisted expert segmentation

Procedures for finite element mesh generation from medical imaging: application to the intervertebral disc

Dissertação de mestrado integrado em Engenharia BiomédicaThe paramount goal of this ‘half-year’ work is the development of a set of methodologies and procedures for the geometric modelling by a finite element (FE) mesh of the bio-structure of a motion segment (or functional spinal unit), i.e., two vertebrae and an intervertebral disc, from segmented medical images (processed from medical imaging). At an initial stage, a three-dimensional voxel-based geometric model of a goat motion segment was created from magnetic resonance imaging (MRI) data. An imaging processing software (ScanIP/Simplewire) was used for imaging segmentation (identification of different structures and tissues), both in images with lower (normal MRI) and higher (micro-MRI) resolutions. It shall be noticed that some soft-tissues, such as annulus fibrosus or nucleus pulposus, are very hard to isolate and identify given that the interface between them is not clearly defined. At the end of this stage, images with different resolutions allowed to generate different 3D voxel-based geometric models. Thereafter, a procedure for the FE mesh generation from the aforementioned voxelized data should be studied and applied. However, as the original geometry was only approximately known from real medical imaging, it was difficult to objectively quantify the quality of the FE meshing procedure and the accuracy between source geometry and target FE mesh. In order to overcome such difficulties, and due to the lack of quality of the available medical imaging, a “virtualization” procedure was developed to create a set of segmented 2D medical images from a well-defined geometry of a motion segment. The main idea was to create the conditions to quantify the quality and the accuracy of the developed FE meshing procedure, as well to study the effect of imaging resolution. Starting from the virtually generated 2D segmented images, a 3D voxel-based structure was achieved. Given that initial domains are now clearly defined, there is no need for further image processing. Then, a two-step FE mesh generation procedure (generation followed by simplification) allows to create an optimized tetrahedral FE mesh directly from 3D voxelized data. Finally, because the virtualization procedure allowed to know the initial geometry, one is able to objectively quantify the quality and the accuracy of the final simplified tetrahedral FE mesh, and thus to understand and quantify: a) the role of the medical image resolution on the FE geometrical reconstruction, b) the procedure and parameters of the FE mesh generation step, and c) the procedure and parameters of the FE mesh simplification step, and thus to give a clear contribution in the definition of the procedure for the FE mesh generation from medical imaging in case of an intervertebral disc.O objetivo fundamental deste trabalho de seis meses é o desenvolvimento de um conjunto de metodologias e procedimentos para a modelação geométrica, através de uma malha de elementos finitos (EF) de uma bio-estrutura de um motion segment (ou unidade funcional da coluna), ou seja, duas vértebras e um disco intervertebral, a partir de imagens médicas segmentadas (processadas a partir de imagiologia médica). Numa fase inicial, um modelo geométrico tridimensional baseado em voxels de um motion segment de uma cabra foi criado a partir de informação de imagens médicas de ressonância magnética (RM). Um software de processamento de imagem (ScanIp/Simplewire) foi usado para segmentação de imagens (identificação de diferentes estruturas e tecidos), em imagens de menor (RM normal) e maior (micro-RM) resolução. Deve ser referido que alguns tecidos moles, como o anel fibroso e o núcleo pulposo são muito difíceis de isolar e identificar, dado que as fronteiras destes não estão claramente definidas. No final desta etapa, as imagens com diferentes resoluções permitiram gerar diferentes modelos geométricos 3D baseados em voxels. Posteriormente, um procedimento para geração de malha de EF, a partir da informação voxelizada acima mencionada, deveria ser estudado e aplicado. No entanto, como a geometria original era aproximadamente conhecida a partir de imagens médicas reais, foi difícil quantificar objetivamente a qualidade do procedimento de geração de malha de EF e a precisão entre a geometria de origem e a malha de EF de destino. A fim de superar tais dificuldades, e devido à falta de qualidade de imagens médicas disponíveis, um procedimento de “virtualização” foi desenvolvido para criar um conjunto de imagens médicas 2D segmentadas a partir de uma geometria de um motion segment bem conhecida. A principal ideia foi criar as condições para quantificar a qualidade e a precisão do procedimento de geração de malha de EF desenvolvido, bem como estudar o efeito da resolução da imagem médica. A partir das imagens 2D segmentadas, geradas virtualmente, uma estrutura de voxels 3D pode ser conseguida. Dado que os domínios iniciais estão agora claramente definidos, não há necessidade de processamento de imagem adicional. Por conseguinte, um procedimento de geração de malha de EF de duas etapas (geração seguida por simplificação) permite criar uma malha de EF tetraédrica otimizada diretamente a partir de informação 3D voxelizada. Por fim, como o procedimento de virtualização permitiu conhecer a geometria inicial, é possível quantificar objetivamente a qualidade e exatidão da malha de EF tetraédrica final simplificada, e assim, compreender e quantificar: a) o papel da resolução da imagem médica na reconstrução geométrica de EF; b) o procedimento e os parâmetros da etapa de geração de malha de EF; c) o procedimento e os parâmetros da etapa de simplificação de malhas de EF, e assim, dar uma contribuição clara na definição do procedimento para a geração de malha de EF a partir de imagem médica, no caso de um disco intervertebral.European Project : NP Mimetic - Biomimetic Nano-Fiber Based Nucleus Pulposus Regeneration for the Treatment of Degenerative Disc Disease, funded by the European Commission under FP7 (grant NMP3-SL-2010-246351

Probabilistic and geometric shape based segmentation methods.

Image segmentation is one of the most important problems in image processing, object recognition, computer vision, medical imaging, etc. In general, the objective of the segmentation is to partition the image into the meaningful areas using the existing (low level) information in the image and prior (high level) information which can be obtained using a number of features of an object. As stated in [1,2], the human vision system aims to extract and use as much information as possible in the image including but not limited to the intensity, possible motion of the object (in sequential images), spatial relations (interaction) as the existing information, and the shape of the object which is learnt from the experience as the prior information. The main objective of this dissertation is to couple the prior information with the existing information since the machine vision system cannot predict the prior information unless it is given. To label the image into meaningful areas, the chosen information is modelled to fit progressively in each of the regions by an optimization process. The intensity and spatial interaction (as the existing information) and shape (as the prior information) are modeled to obtain the optimum segmentation in this study. The intensity information is modelled using the Gaussian distribution. Spatial interaction that describes the relation between neighboring pixels/voxels is modelled by assuming that the pixel intensity depends on the intensities of the neighboring pixels. The shape model is obtained using occurrences of histogram of training shape pixels or voxels. The main objective is to capture the shape variation of the object of interest. Each pixel in the image will have three probabilities to be an object and a background class based on the intensity, spatial interaction, and shape models. These probabilistic values will guide the energy (cost) functionals in the optimization process. This dissertation proposes segmentation frameworks which has the following properties: i) original to solve some of the existing problems, ii) robust under various segmentation challenges, and iii) fast enough to be used in the real applications. In this dissertation, the models are integrated into different methods to obtain the optimum segmentation: 1) variational (can be considered as the spatially continuous), and 2) statistical (can be considered as the spatially discrete) methods. The proposed segmentation frameworks start with obtaining the initial segmentation using the intensity / spatial interaction models. The shape model, which is obtained using the training shapes, is registered to the image domain. Finally, the optimal segmentation is obtained using the optimization of the energy functionals. Experiments show that the use of the shape prior improves considerably the accuracy of the alternative methods which use only existing or both information in the image. The proposed methods are tested on the synthetic and clinical images/shapes and they are shown to be robust under various noise levels, occlusions, and missing object information. Vertebral bodies (VBs) in clinical computed tomography (CT) are segmented using the proposed methods to help the bone mineral density measurements and fracture analysis in bones. Experimental results show that the proposed solutions eliminate some of the existing problems in the VB segmentation. One of the most important contributions of this study is to offer a segmentation framework which can be suitable to the clinical works